Simplify the following expression and state the condition under which the simplification is valid. $y = \dfrac{k^2 - 16}{k - 4}$
First factor the polynomial in the numerator. The numerator is in the form ${a^2} - {b^2}$ , which is a difference of two squares so we can factor it as $({a} + {b})({a} - {b})$ $ a = k$ $ b = \sqrt{16} = -4$ So we can rewrite the expression as: $y = \dfrac{({k} {-4})({k} + {4})} {k - 4} $ We can divide the numerator and denominator by $(k - 4)$ on condition that $k \neq 4$ Therefore $y = k + 4; k \neq 4$